Curriculum Focus Document
Calculus
Chapter 1: Limits and Their Properties
GOAL(S)
This unit will address the following relevant goals:
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Students find limits graphically, numerically and analytically
Students will analyze continuity and one-sided limits of functions
Students will determine infinite limits from left and right
Students will find and sketch vertical asymptotes of functions
UNDERSTANDING(S)
Students will understand the following:
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The properties of limits and continuity of functions as tools to develop derivatives and integrals.
How to change between numerical, analytical, graphical and verbal forms of limits and continuity.
ESSENTIAL QUESTION(S)
Students will engage in deep thought on the following:
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How do we view the role of Calculus on describing how rapidly things change?
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How do we graph the functions that arise in scientific study including lines, quadratic functions,
square roots, and basic trigonometric functions?
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How do we use the absolute value function and how do we define its intervals?
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How do we define and calculate slopes utilizing the derivative of a function?
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How do we define derivatives and extend that to velocity and acceleration?
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How do we describe a special class of functions called continuous functions?
KNOWLEDGE (CP)
SKILLS (CP)
Students will know the following:
Students will be able to do the following:

Graphical and Numerical Limits


Analytical Limits


Continuity and One-sided limits


Infinite limits

Determining the existence and value of limits
graphically and numerically
Determine the existence and value of limits
analytically
Analyze functions for continuity
Determine limits at positive and negative
infinity and use them to sketch vertical
asymptotes
This publication is the property of Antonian College Preparatory High School. Duplication in whole or
part, outside of ACPHS, is prohibited with express written permission from ACPHS.
Curriculum Focus Document
KNOWLEDGE (H/AP)
SKILLS (H/AP)
Students will know the following:
Students will be able to do the following:

Graphical and Numerical Limits


Analytical Limits


Continuity and One-sided limits


Infinite Limits

Determining the existence and value of limits
graphically and numerically
Determine the existence and value of limits
analytically
Analyze functions for continuity
Determine limits at positive and negative
infinity and use them to sketch vertical
asymptotes

This publication is the property of Antonian College Preparatory High School. Duplication in whole or
part, outside of ACPHS, is prohibited with express written permission from ACPHS.